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Collaborative Spectrum Sensing Overcome hidden terminal problem Multiple cognitive radio observe together 1- the SUs perform Local Sensing of PU signal 2- the SUs send their Local Sensing bits to a common fusion center 3- Fusion Center makes final decision: PU present or not

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Problem 2: Dynamic Spectrum Access Adjust spectrum resource usage in the near-real-time manner in response to changes in the users’ objectives, changes of radio states, and changes in the environment and external constraints.

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Problem 3: Exploration and Exploitation Exploitation: the immediate benefit gained from accessing the channel with the estimated highest reward Exploration is the process by which the cognitive users tend to probe more channels to discover better channel opportunities. Example: should find new topics or study the current topics

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Game Theory Overview What is game theory? –The formal study of conflict or cooperation –Modeling mutual interaction among rational decision makers –Widely used in economics Components of a “game” –Rational players with conflicting interests or mutual benefit –Strategies or actions –Utility as a payoff of player’s and other players’ actions –Outcome: Nash Equilibrium Many types –Non-cooperative game theory –Cooperative game theory –Dynamic game theory –Stochastic game –Auction theory

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Coalitional Games: Preliminaries Definition of a coalitional game (N,v) –A set of players N, a coalition S is a group of cooperating players ( subset of N ) –Worth (utility) of a coalition v u In general, v(S) is a real number that represents the gain resulting from a coalition S in the game (N,v) u v(N) is the worth of forming the coalition of all users, known as the grand coalition –User payoff x i : the portion of v(S) received by a player i in coalition S Characteristic form –v depends only on the internal structure of the coalition –Most common form of coalitional games Partition form –v depends only on the whole partition currently in place –Hard to solve, still under thorough research in game theory Graph form –The value of a coalition depends on a graph structure that connects the coalition members 14

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Coalitional Games: Utility Transferable utility (TU) –The worth v(S) of a coalition S can be distributed arbitrarily among the players in a coalition hence, –v(S) is a function from the power set of N over the real line –Example: Money, Euro/dollar/RMB… Non-transferable utility (NTU) –The payoff that a user receives in a coalition is pre-determined, and hence the value of a coalition cannot be described by a function –v(S) is a set of payoff vectors that the players in S can achieve –Example: channel

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An example coalitional game Example of a coalition game: Majority Vote –President is elected by majority vote –A coalition consisting of a majority of players has a worth of 1 since it is a decision maker –Value of a coalition does not depend on the external strategies of the users u This game is in characteristic function form –If the voters divide the value as money u Transferable utility

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A new classification - The grand coalition of all users is an optimal structure. -Key question “How to stabilize the grand coalition?” - Several well-defined solution concepts exist. - The network structure that forms depends on gains and costs from cooperation. -Key question “How to form an appropriate coalitional structure (topology) and how to study its properties?” - More complex than Class I, with no formal solution concepts. - Players’ interactions are governed by a communication graph structure. -Key question “How to stabilize the grand coalition or form a network structure taking into account the communication graph?” - Solutions are complex, combine concepts from coalitions, and non- cooperative games

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Class I: Canonical Coalitional Games Main properties –Cooperation is always beneficial u The grand coalition is guaranteed to form –The game is superadditive –The most famous type of coalitional games! Main Objectives –Study the properties and stability of the grand coalition u How can we stabilize the grand coalition? –How to divide the utility and gains in a fair manner ? u Improper payoff division => incentive for players to leave coalition

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Canonical games: Solution concepts The Core: the most renowned concept –For a TU game, the core is a set of payoff allocation (x 1,..., x N ) satisfying two conditions –The core can be empty u A non-empty core in a superadditive game => stable grand coalition The drawbacks of the core –The core is often empty. –When the core is non-empty it is often a large set. –The allocations that lie in the core are often unfair.

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Main Idea CR nodes help the PU node reduce transmission power using cooperative transmission, for future rewards of transmission. The idea can be formulated by a coalition game. To get a good position, try to volunteer first CR users PR transmission

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Class II: Coalition Formation Games Main Properties –The game is NOT superadditive –Cooperation gains are limited by a cost u The grand coalition is NOT guaranteed to form –Cluster the network into partitions –New issues: network topology, coalition formation process, environmental changes, etc Key Questions –How can the users form coalitions? –What is the network structure that will form? –How can the users adapt to environmental changes such as mobility, the deployment of new users, or others? –Can we say anything on the stability of the network structure?

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Coalition Formation: Merge and Split Merge rule: merge any group of coalitions where Split rule: split any group of coalitions where A decision to merge (split) is an agreement between all players to form (break) a new coalition –Socialist (social well fare improved by the decision) –Capitalist (individual benefit improved)

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Merge and Split: Properties Any merge and split iteration converges and results in a final partition. Merge and split decision –Individual decision –Coalition decision –Can be implemented in a distributed manner with no reliance on any centralized entity Using the Pareto order ensures that no player is worse off through merge or split –Other orders or preference relations can be used

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Stability Notions D hp stable –No users can defect via merge/split –Partition resulting from merge and split is D hp stable D c stable –No users can defect to form a new collection in N –A D c stable partition is socially optimal –When it exists, it is the unique outcome of any merge and split iteration –Strongest type of stability

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Class III: Coalition Graph Games Main properties –The game is in graph form u May depend on externalities also –There is a graph that connects the players of every coalition –Cooperation with or without cost –A Hybrid type of games: concepts from classes I and II, as well as non- cooperative games

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Coalition Graph Games First thought of by Myerson, 1977, called “Coalitional games with communication structure” –Axiomatic approach to find a Shapley-like value for a coalitional game with an underlying graph structure –Coalition value depends on the graph –The dependence is only based on connections Key Questions –How can the users form the graph structure that will result in the network? –If all players form a single graph (grand coalition with a graph), can it be stabilized? –How can the users adapt to environmental changes such as mobility, the deployment of new users, or others? –What is the effect of the graph on the game?

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Hierarchical Network Formation Multi-hop hierarchical networks LTE and WiMAX 802.16j We consider uplink transmission How to determine the hierarchies? We assume a fixed distance-based hierarchy division Others divisions can be accommodated How to form the tree topology? Network formation games New concept of hierarchial Nash equilibrium Routing in communication networks See the work by Johari (Stanford) Many future possibilities The formation of graphs is ubiquitous in the context of networks

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Summary of coalitional game Cognitive radio network and its basic problems Coalitional games are a strong tool for different models in wireless and communication networks A novel classification that can help in identifying potential applications A tool for next generation self-organizing networks –Especially through coalition formation and network formation games Try to find collaboration among experts here Try to sell books